Numerical Methods Elements of Electromagnetics Fourth Edition Sadiku

Numerical Methods Elements of Electromagnetics Fourth Edition Sadiku 1

Figure 14. 1 A small displacement on a field line. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 2

Figure 14. 2 Generated points on E-field lines (shown thick) and equipotential lines (dotted). Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 3

Figure 14. 3 Computer program for Example 14. 1. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 4

Figure 14. 3 (Continued) Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 5

Figure 14. 3 (Continued) Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 6

Figure 14. 3 (Continued) Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 7

Figure 14. 4 For Example 14. 1; plots of E-field lines and equipotential lines due to (a) two point charges and (b) four point charges (a two-dimensional quadrupole). Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 8

Figure 14. 5 For Practice Exercise 14. 1. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 9

Figure 14. 6 Finite difference solution pattern: (a) division of the solution into grid points, (b) finite difference five-node molecule. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 10

Figure 14. 7 Finite difference solution pattern for the wave equation: eq. (14. 19). Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 11

Figure 14. 8 For Example 14. 2. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 12

Figure 14. 9 Computer program for Example 14. 2. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 13

Figure 14. 10 For Example 14. 2: plot of F(x). Continuous curve is for N = 10; dashed curve is for N = 4. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 14

Figure 14. 11 For Example 14. 3. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 15

Figure 14. 12 For Example 14. 3; the values not crossed out are the solutions after five iterations. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 16

Figure 14. 13 For Practice Exercise 14. 3. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 17

Figure 14. 14 For Example 14. 4. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 18

Figure 14. 15 For Example 14. 4; a 15 ´ 10 grid. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 19

Figure 14. 16 Computer program for Example 14. 4. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 20

Figure 14. 16 (Continued) Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 21

Figure 14. 17 For Practice Exercise 14. 4. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 22

Figure 14. 18 Thin conducting wire held at a constant potential. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 23

Figure 14. 19 Division of the wire into N segments. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 24

Figure 14. 20 Matlab code for calculating the charge distribution on the wire in Figure 14. 18. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 25

Figure 14. 21 Plot of r. L against y. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 26

Figure 14. 22 Parallel-plate capacitor; for Example 14. 5. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 27

Figure 14. 23 Subsections i and j; for Example 14. 5. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 28

Figure 14. 24 Matlab program for Example 14. 5. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 29

Figure 14. 24 (Continued) Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 30

Figure 14. 25 Parallel conducting wires for Practice Exercise 14. 5. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 31

Figure 14. 26 A typical finite element subdivision of an irregular domain. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 32

Figure 14. 27 Typical triangular element; the local node numbering 1 -2 -3 must be counterclockwise as indicated by the arrow. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 33

Figure 14. 28 Shape functions a 1 and a 2 for a triangular element. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 34

Figure 14. 29 Assembly of three elements: i-j-k corresponds to local numbering 1 -2 -3 of the element in Figure 14. 27. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 35

Figure 14. 30 For Example 14. 6: (a) two-element mesh, (b) local and global numbering of the elements. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 36

Figure 14. 31 For Practice Exercise 14. 6. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 37

Figure 14. 32 For Example 14. 7: (a) two-dimensional electrostatic problem, (b) solution region divided into 25 triangular elements. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 38

Figure 14. 33 Computer program for Example 14. 7. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 39

Figure 14. 33 (Continued) Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 40

Figure 14. 34 For Practice Exercise 14. 7. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 41

Figure 14. 35 (a) Shielded double trip line with partial dielectric support. (b) Problem in (a) simplified by taking advantage of symmetry. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 42

Figure 14. 36 Computation molecule for Laplace’s equation. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 43

Figure 14. 37 Interface between media of dielectric permittivities e 1 and e 2. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 44

Figure 14. 38 Computation molecules used for satisfying symmetry conditions: (a) ¶V/dx = 0, (b) ¶V/dy = 0. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 45

Figure 14. 39 The rectangular path ℓ used in calculating a charge enclosed. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 46

Figure 14. 40 Matlab code for Example 14. 8. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 47

Figure 14. 40 (Continued) Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 48

Figure 14. 40 (Continued) Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 49

Figure 14. 41 For Review Questions 14. 3 and 14. 10. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 50

Figure 14. 42 Finite difference grid in cylindrical coordinates; for Problem 14. 5. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 51

Figure 14. 43 For Problem 14. 7. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 52

Figure 14. 44 For Problem 14. 9. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 53

Figure 14. 45 For Problem 14. 10. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 54

Figure 14. 46 For Problem 14. 11. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 55

Figure 14. 47 For Problem 14. 12. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 56

Figure 14. 48 For Problem 14. 13. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 57

Figure 14. 49 For Problem 14. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 58

Figure 14. 50 For Problem 14. 17. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 59

Figure 14. 51 For Problem 14. 18. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 60

Figure 14. 52 For Problem 14. 20. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 61

Figure 14. 53 Analysis of strip transmission line using moment method; for Problem 14. 21. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 62

Figure 14. 54 For Problem 14. 22. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 63

Figure 14. 55 For Problem 14. 23; coaxial line of (a) arbitrary cross section, (b) elliptical cylindrical cross section. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 64

Figure 14. 56 For Problem 14. 24. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 65

Figure 14. 57 For Problem 14. 25. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 66

Figure 14. 58 Triangular elements of Problem 14. 26. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 67

Figure 14. 59 For Problem 14. 27. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 68

Figure 14. 60 For Problem 14. 28. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 69

Figure 14. 61 For Problem 14. 29. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 70

Figure 14. 62 For Problem 14. 30. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 71

Figure 14. 63 For Problems 14. 31 and 14. 32. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 72

Figure 14. 64 For Problem 14. 33. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 73

Figure 14. 65 For Problem 14. 34. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 74

Figure 14. 66 For Problem 14. 37. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 75

Figure 14. 67 For Problem 14. 38. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 76

Figure 14. 68 For Problem 14. 39. Elements of Electromagnetics Fourth Edition Sadiku Copyright © 2007 Oxford University Press 77